The solution for one type
The solution for one type of this system approximates the Hamiltonian as the product of an operator and its Hermitian conjugate. The ground state energy for one type of this system equals h-bar times omega over two, via the solution to the Schrodinger equation. Another type of this system involves a second-order differential equation, which gives the solution that the position is a sinusoidal function of time. For 10 points, the pendulum and mass-on-a-spring are types of what system that comes in "quantum" and "simple" types?
The solution for one type of this system approximates the Hamiltonian as the product of an operator and its Hermitian conjugate.
{harmonic oscillator} [or quantum {harmonic oscillator;} or simple {harmonic oscillator}]